Question

After how many decimal places will the decimal expansion of the number $\frac{5^3}{2^3.5^4}$ terminate? Justify your answer without performing the actual division.

Answer 1

The decimal expansion of the number $\frac{5^3}{2^3{.5}^4}$ will terminate after $3$ decimal places.

$\frac{5^3}{2^3{.5}^4}=\frac{1}{2^3{.5}^{4-3}}=\frac{1}{8\times 5}$

$=\frac{1}{40}=0.025$.

Hence, the decimal will terminate after $3$ decimal place.